avelength of light is 389.0 nm and its frequency is 7.707times 10^14 Hz. Show how this frequency value was calculated.

To calculate the frequency of light given its wavelength, we can use the formula:<br /><br />\[ \text{Frequency} = \frac{\text{Speed of light}}{\text{Wavelength}} \]<br /><br />The speed of light in a vacuum is approximately \( 3.00 \times 10^8 \) meters per second (m/s).<br /><br />Given:<br />- Wavelength (\( \lambda \)) = 389.0 nm<br />- Speed of light (\( c \)) = \( 3.00 \times 10^8 \) m/s<br /><br />First, we need to convert the wavelength from nanometers to meters:<br /><br />\[ 1 \text{ nm} = 10^{-9} \text{ m} \]<br /><br />So,<br /><br />\[ \lambda = 389.0 \text{ nm} \times 10^{-9} \text{ m/nm} = 3.89 \times 10^{-7} \text{ m} \]<br /><br />Now, we can calculate the frequency:<br /><br />\[ \text{Frequency} = \frac{3.00 \times 10^8 \text{ m/s}}{3.89 \times 10^{-7} \text{ m}} \]<br /><br />\[ \text{Frequency} = \frac{3.00 \times 10^8}{3.89 \times 10^{-7}} \]<br /><br />\[ \text{Frequency} \approx 7.707 \times 10^{14} \text{ Hz} \]<br /><br />Therefore, the frequency of the light with a wavelength of 389.0 nm is approximately \( 7.707 \times 10^{14} \) Hz.